(* EVALUATION FOR CONTEXT-SENSITIVE PARALLEL R-TRANSITION ON TERMS **********)
-(* Properties with strong normalization for unbound rt-transition for terms *)
+(* Properties with strongly normalizing terms for extended rt-transition ****)
(* Basic_1: was just: nf2_sn3 *)
(* Basic_2A1: was: csx_cpre *)
lemma cprre_total_csx (h) (G) (L):
- ∀T1. ❪G,L❫ ⊢ ⬈*[h] 𝐒❪T1❫ → ∃T2. ❪G,L❫ ⊢ T1 ➡*[h] 𝐍❪T2❫.
+ ∀T1. ❪G,L❫ ⊢ ⬈*𝐒 T1 → ∃T2. ❪G,L❫ ⊢ T1 ➡*𝐍[h,0] T2.
#h #G #L #T1 #H
@(csx_ind … H) -T1 #T1 #_ #IHT1
elim (cnr_dec_teqx h G L T1) [ /3 width=3 by ex_intro, cpmre_intro/ ] *
#T0 #HT10 #HnT10
-elim (IHT1 … HnT10) -IHT1 -HnT10 [| /2 width=2 by cpm_fwd_cpx/ ]
+elim (IHT1 … HnT10) -IHT1 -HnT10 [| /2 width=3 by cpm_fwd_cpx/ ]
#T2 * /4 width=3 by cprs_step_sn, ex_intro, cpmre_intro/
qed-.